Abstract: Genetic algorithms based on real （floating） coded （FGAs） have received a great deal of attention regarding their potential as optimization techniques for complex functions, but the complete convergent results are still rare. In this paper, the convergence of FGAs used in most applications is analyzed and some general conclusions are obtained under best individual preservation strategy. Then by using them the convergence of FGAs is examined when using ordinary mutation and crossover operators. These results not only give useful convergence conclusions but also provide more insights into operators and give help to design adaptation operators. Besides, the process and results still hold true when discussing the convergence of EP（evdutionary programming） and ESs（evdutionary strategies）.